As you might have noticed, Blender has a new render-engine called Cycles which is fundamentally different from the old-but-gold Blender Internal renderer. The main feature of Cycles is that it is based on path-tracing (simulating the rays/photons) which makes it a lot easier to get certain effects necessary for photo-realism (such as light turning into a rainbow when hitting a glass-prism). Here are some basic advice.

Steps

1

Change your render Engine at the dropdown-menu where it says "Blender Render" and select "Cycles Render"

2

Materials are now node-based, so start by splitting the window, setting one to node-editor and clicking on the material-icon of the new window, if it isn't selected by default..

If this is an old .blend you might already have assigned materials and want to click on "use nodes" in the material settings

Otherwise add a new material

Now things are getting a bit confusing because of the number of different combinations. The best way to get used to this system would be to memorize which shade gives which effect and mixing & optimizing them by textures and Mix - nodes (which you should know from the compositor).[1]

3

After you have experimented with the new materials and probably set up a few lamps by adding an Emission shader to a mesh (most likely a plain out of the camera-sight) you can tweaking the render-settings:

The only new setting is ether "Interior" or "Sampling" and "Light Paths" depending on the version of Blender you use

"Samples:Render:" is the number on which the render time depends most. On 0 it will render until Esc is pressed

"Bounces min/max", "Transparency min/max", "Diffuse", "Glossy"... are for the tuning if the result is still very noisy it might have something to do with all the Glossy materials you set up in the scene and might get better if you adjust these values

"Performance/Acceleration structure" has some settings which are essential for animations like "cache BVH"

Community Q&A

Tips

Fireflies have a nearly infinite amount of energy so you might be able to mask them out with the "math/less than" node in the compositor

Try to enable GPU rendering if you got a pretty modern nVidia card ("user preferences/system/compute device/CUDA/Your Graphic card(s)"). It will make the rendering a lot faster

By changing the seed in the render settings you get a different noise-pattern so you can stop and restart a render simply by saving the images & increasing the seed after a stop and mixing them back together afterwards

You still can and should use the compositor

Warnings

Everything might change in the next major update (especially button positions)

Just avoid glass material because it produces a lot of fireflies (static white pixels) right now and can be faked pretty easily if you mix a glossy shader with a transparent one and use as a Factor "Lightpath/glossy"